Zadanie 1a
State the mode.
Matematyka AA IB HL — maj 2026, TZ2, Paper 2 (zadania wzorowane)
Zadania wzorowane na pytaniach z tego arkusza: te same umiejętności, format i punktacja, inne dane i kontekst. Treści arkusza IB nie publikujemy.
W bazie 34 zadania z tego arkusza, razem 110 punktów, każde z kluczem i schematem punktowania.
Zadanie 1b
Find (i) the mean; (ii) the median; (iii) the population standard deviation.
Zadanie 1c
Draw a box-and-whisker plot on the scale provided.
- Materiał graficzny
Zadanie 2a
Show that h = 720/(πr2).
Zadanie 2b
Show that A = πr2 + 1440/r.
Zadanie 2c
Use a graph or another method to find (i) the least material area; (ii) the corresponding radius.
Zadanie 3a
Find the initial velocity.
Zadanie 3b
Find the total distance travelled during the first six seconds.
Zadanie 3c
Find the time when acceleration is 17 m/s².
Zadanie 4a
Find p.
Zadanie 4b
Find P(X = 12 ∣ X ≥ 9).
Zadanie 5
The region bounded by the y-axis, y=5, y=10 and y = 30/(x + 2) is rotated through a full turn about the y-axis. Find the resulting solid’s volume.
Zadanie 6a
Find a exactly.
Zadanie 6b
Find Var(X).
Zadanie 7a
Find k for which there are infinitely many solutions.
Zadanie 7b
For this k, (i) interpret the solutions geometrically; (ii) express them parametrically.
Zadanie 8a
Prove algebraically that f is odd.
- Materiał graficzny
Zadanie 8b
(i) Show that c=4b and a=12b. (ii) Hence deduce f(x) = 12x/(x2 + 4).
Zadanie 9a
Show that .
Zadanie 9b
Use 9a and the substitution u=cos2x to evaluate .
Zadanie 10a
For a randomly selected type-R battery find the probability that its duration is (i) below 224 minutes; (ii) between 224 and 242 minutes; (iii) between 224 and 242 minutes given it exceeds 224 minutes.
Zadanie 10b
For type S, P(S<200)=0.30854 and P(200<S<224)=0.62465. Find μ and σ.
Zadanie 10c
For type S, P(S<200)=0.30854 and P(200<S<224)=0.62465. Independently select one battery of each type. Find the probability that at least one lasts more than 224 minutes.
Zadanie 11a
Find (i) ; (ii) hence or otherwise the area of ABC.
- Materiał graficzny
Zadanie 11b
Show that K = (4/3, 4/3, 2).
Zadanie 11c
The base plane Π is 4x − y + 7z = 18. State a vector equation for its perpendicular L₁ through K.
Zadanie 11d
The apex is H = (8/3, 1, 13/3). Find the pyramid’s volume.
Zadanie 11e
Let . Find its acute angle with Π to the nearest degree.
Zadanie 11f
Show that L₁ and L₂ are skew.
Zadanie 12a
Sketch y=f(x), giving the equations of all asymptotes.
Zadanie 12b
(i) Describe a sequence of transformations taking y=arctan x to y=f(x). (ii) State the inflection point.
Zadanie 12c
(i) Find f⁻¹(x) and its domain. (ii) Find the intersection of y=f(x) and y=f⁻¹(x) with x>0.
Zadanie 12d
Find the tangent equation at x=2.
Zadanie 12e
The tangent referred to here is the tangent to y=f(x) at x=2. This tangent meets the curve again at a point P distinct from the tangency point. Find (i) P; (ii) the enclosed area.